Anna Maxted and her sons Conrad, left, and Caspar, with Natasha the cat, sister of Disco. Photograph: Frank Baron for the Guardian

I can vividly recall the rapturous joy, the first time he was placed in my arms, 15 years ago – I felt something in my heart twist: the physical sensation of falling in love. In an emotional sense, he was my first child – only this baby was furry, with whiskers and a tail.

Disco, a handsome tiger-striped Bengal, was friendly, boisterous, good-natured – he provided us with a decade and a half of affection and pleasure. He loved people, especially me, and as my husband said, "He wasn't really a cat. He was a person disguised as a cat."

Half of those reading will now be choked with irritation and disdain – odd that some can't stretch to imagine the blessing of a companion animal; a little piece of uncomplicated goodness in one's life.

Disco died suddenly a month ago, and I'm still in shock. The whole family feels subdued. It's strange, the death of a pet – privately, people admit, "I felt as if I'd lost a baby" or "We're all are utterly devastated" – and yet that minority and their open sniggers hold social dominance, reducing this brand of grief to shameful and embarrassing.

They find it offensive that some should feel so deeply for a creature and grieve its death – as if by doing so we're disrespecting anyone bereaved of a person. I'm not sure why the two can't co-exist. I'm not gate-crashing funerals in a black veil.

Anyway, regardless of their opinions, this other grief does exist, only dismissive comments kindly meant – "Poor little chap; chin up!" or "This brings up other losses" – mean that those afflicted stop talking about it.

I dreaded telling the seven year old, who often refused to sleep unless Disco was curled on his bed, that he wasn't coming back from the vet. When I did, Conrad gave a primal wail and sank to the ground. The depth of his emotion scared me – I didn't want to deny, or aggravate it. I told him, "This is the saddest thing that has ever happened to you and it's a horrible, painful feeling." Then I said, "But that cat had the loveliest life – and you were all his kittens."

Disco and his sister Natasha had lived in stately elegance for five years, when we brought our first (human) child back from hospital – Natasha was asleep in the Swedish cot as if it were a giant cat basket. A stiff adjustment period followed, but even though, as a friend warned "Toddlers dislike cats; they pull their tails" in 10 years of being noisily harassed, yanked about like concertinas, and accidentally included in cricket games by three boys, those cats couldn't have been more cosseted if we were ancient Egyptians.

The children vied over whose lap he would choose, and Disco wasn't just patient; he sought out their company.

The house feels empty without him sprawled on the kitchen counter, narrowing his green eyes in the hope that prawns will come of it. There are fewer moments of joy in my day. A cat was not a casual extra, but an essential – he was a cherished part of the family. I miss him in that restless way of grief, when you can't settle – when you think that surely, if you want something badly enough not to be true, it can't be.

Balance is provided in the form of my husband – who often worked on his laptop from an awkward, twisted horizontal position on the sofa, so Disco could sleep on his chest, but feels incapable of devoting much sadness to his demise.

When I told him that there's an Animal Samaritans charity to provide "support and understanding" for those grieving for a pet, he laughed, saying he imagined a man mournfully holding a water-filled plastic bag containing a floating goldfish. He'll admit that Disco was "one of the most beautiful creatures on this earth, and one of the nicest", yet in the same breath, exclaim, incredulous, "Cats have shorter lives than people! Surely you knew that when you got him?"

But I feel like our five year old, who sobbed, "I wish there was no such thing as dying!" Caspar feels the loss sporadically, but deeply – so much that his reception teacher worked through a storybook on grief with him: he brought home a heart-breaking eulogy he'd dictated to the wonderful Miss Potter ("I liked his brown skin and black spots"). At the end of it, he'd scrawled, "I wish you good luck, Disco." For a week, there was talk of heaven, and wanting us all to go there.

I can't think of that cat without welling up. As my mother insultingly put it, "It was very flattering to have someone who never criticised you and depended on you completely."

Yes, it was. I agree. But it was his personality. That's what you non-pet people don't understand. With respect to Natasha (she's more aloof, Disco understood the job description), I've vowed to return to the breeder, and find a replica of my friend in kitten form – leading my husband to accuse me of being "like Rod Stewart choosing a wife".

Harsh words, but I've seen him surreptitiously glance towards the back door – Disco preferred butler service to using the flap. He might joke about blondes but, in his heart, he knows we've lost a beloved family member.